Pruning and training: Avoid making this a big chore by choosing plants that don't need a lot of complicated pruning, and choosing climbers that don't need to be tied to their supports. Formal hedges or topiaries that require frequent trimming can also be more work than you'd like; try opting for a more informal hedge of plants that won't outgrow the space you have.
Watering: Planting drought-tolerant (xeriscape) plants can help reduce the time spent watering, as well as mulching the soil to keep moisture in. However, when watering does need to be done, a sprinkler, soaker hose or drip irrigation system connected to an automatic timer can make it automatic, and you don't even have to remember to turn the water off when it's finished.
Mowing the lawn: Install a mow strip around your lawn to eliminate the chore of trimming the edges. Make sure the lawn edges are long curves instead of corners; this makes it much easier to maneuver. In fact, the most efficient shape for a lawn is a circle, since the mower would never have to turn around. If there are trees or shrubs in the lawn, consider joining them into a large bed that is easier to mow around.
Grow the right plants: Whenever possible, plant trees, shrubs and perennials instead of annuals that must be replanted every year, unless they will reseed themselves. Trees and shrubs generally require less maintenance than perennials, which must often be divided every few years. Choose varieties that are sturdy and/or compact to avoid the need for staking, and also look for varieties that are "self-cleaning" and don't need to be deadheaded.
Digging: Some methods of vegetable growing advocate turning the soil to a depth of one to two feet every year. Most newer methods forgo this intensive labour for some combination of mulching and aerating. I personally feel that a new bed should probably be intensively dug, but after the first year, just dig the holes for the plants to go in.
Weeds and pests: Always pull weeds when they're small, because it's easier, and never let them go to seed, for obvious reasons. Pulling a few weeds as you walk by allows you to keep small problems from becoming big problems. When it comes to insect and disease damage, always start by buying resistant varieties when you can. Planting flowers that provide food for beneficial insects can also keep pests from becoming a big problem, and mesh row covers can keep insects out without resorting to frequent spraying, dusting, or hand-picking. And always try to avoid starting a garden in a problematic area: make sure the quack grass is totally gone before you put your plants in!
By planning for ease of maintenance in plant selection and design, your beautiful garden can require much less maintenance than you might think.